We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (Xν) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach-Saks property, then the deviation from the weak Banach-Saks property of an operator of a certain class between direct sums E(Xν) is equal to the supremum of such deviations attained on the coordinates Xν. This is a quantitative version for operators of the result for the Köthe- Bochner sequence spaces E(X) that if E has the Banach-Saks property, then E(X) has the weak Banach-Saks property if and only if so has X.
@article{bwmeta1.element.doi-10_1515_umcsmath-2015-0005,
author = {Andrzej Kryczka},
title = {Deviation from weak Banach--Saks property for countable direct sums},
journal = {Annales UMCS, Mathematica},
volume = {68},
year = {2015},
zbl = {06418153},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0005}
}
Andrzej Kryczka. Deviation from weak Banach–Saks property for countable direct sums. Annales UMCS, Mathematica, Tome 68 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0005/
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